Problem: If $x \boxdot y = 8x-y$ and $x \bigtriangleup y = 4x-4y$, find $-5 \boxdot (-1 \bigtriangleup 1)$.
Answer: First, find $-1 \bigtriangleup 1$ $ -1 \bigtriangleup 1 = (4)(-1)-(4)(1)$ $ \hphantom{-1 \bigtriangleup 1} = -8$ Now, find $-5 \boxdot -8$ $ -5 \boxdot -8 = (8)(-5)-(-8)$ $ \hphantom{-5 \boxdot -8} = -32$.